MinT - Best Known (85, 144, s)-Nets in Base 9

Best Known (85, 144, s)-Nets in Base 9

(85, 144, 448)-Net over F₉ — Constructive and digital

Digital (85, 144, 448)-net over F₉, using

trace code for nets [i] based on digital (13, 72, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(85, 144, 654)-Net over F₉ — Digital

Digital (85, 144, 654)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 144, 74016)-Net in Base 9 — Upper bound on s

There is no (85, 144, 74017)-net in base 9, because

1 times m-reduction [i] would yield (85, 143, 74017)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28620 824342 185543 557704 986668 618606 108777 374468 563204 107641 980878 189517 814603 339350 833915 404704 606393 699697 399140 044758 645632 270103 375721 > 9¹⁴³ [i]